"He [Obama] said, up until now, and I think correctly - we are not going to act as the Shiite air force, and we're not going to act in a major way on behalf of al-Maliki, because he's a sectarian, and he's wrecked what we left behind," Krauthammer said. "Well, he's now gone. and now there's a replacement."

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After threatening a legal challenge, al-Maliki finally agreed to step aside on Thursday in favor of Haider al-Abadi, the designated prime minister, who was appointed by the Iraqi president earlier in the week. Al-Abadi has one month to form a new government.

Krauthammer, a syndicated columnist and Fox News contributor, said the change in Iraqi leadership will affect Obama's decisions in Iraq going forward.

"The bluff is called," he said. "The U.S. president said, we're going to support Iraq if ISIS is a threat, which it is - a strategic interest to push it back. Well, then he has to deliver, with something he's going to offer Baghdad."

Krauthammer added that Obama must make a decision quickly as ISIS continues to terrorize civilians.

"[Obama] doesn't seem to want to do anything besides protecting our consulate, which he could evacuate tomorrow if he wanted, and doing humanitarian stuff - social work - which, apparently, he says is now un-needed, because miraculously, the Yazidis have gotten off the mountain," Krauthammer said. "So, if this is a strategic issue, if this is a threat to the west, which it obviously is, and he said, I'm waiting for the new government - well, the new government is here. What's he going to do?"